用于边界值问题的拓扑不动点原理

出版时间：2011-7  出版社：世界图书出版公司  作者：安德里斯  页数：761  

内容概要

　　安德里斯编著的《用于边界值问题的拓扑不动点原理》旨在系统介绍凸空间上的单值和多值映射的拓扑不动点理论。内容包括常微分方程的边界值问题和在动力系统中的应用，是第一本用非度量空间讲述拓扑不动点理论的专著。尽管理论上的讲述和书中精选的应用实例相结合，但本身具有很强的独立性。本书利用不动点理论求微分方程的解，独具特色。目次：理论背景；一般原理；在微分方程中的应用。

书籍目录

preface
scheme for the relationship of singlc sections
chapter Ⅰ theoretical background
Ⅰ.1.structure of locally convex spaces
Ⅰ.2.anr-spaces and ar-spaces
Ⅰ.3.multivadued mappings and their selections
Ⅰ.4.admissible mappings
Ⅰ.5.special classes of admissible mappings
Ⅰ.6.lefschetz fixed point theorem for admissible mappings
Ⅰ.7.lefschetz fixed point theorem for condensing mappings
Ⅰ.8.fixed point index and topological degree for admissible maps in
locally convex spaces
Ⅰ.9.noncon/pact case
Ⅰ.10.nielsen number
Ⅰ.11.nielsen number; noncompact case
Ⅰ.12.remarks and comments
chapter Ⅱ general principles
Ⅱ.1.topological structure of fixed point sets:
aronszajn-browder-gupta-type results
Ⅱ.2.topological structure of fixed point sets: inverse limit
method
Ⅱ.3.topological dimension of fixed point sets
Ⅱ.4.topological essentiality
Ⅱ.5.relative theories of lefschetz and nielsen
Ⅱ.6.periodic point principles
Ⅱ.7.fixed point index for condensing maps
Ⅱ.8.approximation methods in the fixed point theory of multivalued
mappings
Ⅱ.9.topological degree defined by means of approximation
methods
Ⅱ.10.continuation principles based on a fixed point index
Ⅱ.11.continuation principles based on a coincidence index
Ⅱ.12.remarks and comments
chapter Ⅲ application to differential equations and
inclusions
Ⅲ.1.topological approach to differential equations and
inclusions
Ⅲ.2.topological structure of solution sets: initial value
problems
Ⅲ.3.topological structure of solution sets: boundary value
problems
Ⅲ.4.poincare operators
Ⅲ.5.existence results
Ⅲ.6.multiplicity results
Ⅲ.7.wakewski-type results
Ⅲ.8.bounding and guiding functions approach
Ⅲ.9.infinitely many subharmonics
Ⅲ.10.almost-periodic problems
Ⅲ.11.some further applications
Ⅲ.12.remarks and comments
appendices
a.1.almost-periodic single-valued and multivalued functions
a.2.derivo-periodic single-valued and multivalued functions
a.3.fractals and multivalued fractals
references
index

章节摘录

版权页：   插图：   Our book is devoted to the topological fixed point theory both for single—valued and multivalued mappings in locally convex spaces， including its application to boundary value problems for ordinary differential equations （inclusions） and to （multivalued） dynamical systems． It is the first monograph dealing with the topological fixed point theory in non—metric spaces． Although the theoretical material was tendentially selected with respect to applications， we wished to have a self—consistent text （see the scheme below）． Therefore， we supplied three appendices concerning almost—periodic and derivo—periodic single—valued （multivalued） functions and （multivalued） fractals． The last topic which is quite new can be also regarded as a contribution to the fixed point theory in hyperspaces． Nevertheless， the reader is assumed to be at least partly familiar in some related sections with the notions like the Bochner integral， the Aumann multivalued integral， the Arzela—Ascoli lemma， the Gronwall inequality， the Brouwer degree， the Leray—Schauder degree， the topological （covering） dimension， the elemens of homological algebra，．．．Otherwise， one can use the recommended literature． Hence， in Chapter I， the topological and analytical background is built． Then， in Chapter II （and partly already in Chapter I）， topological principles necessary for applications are developed， namely： —the fixed point index theory （resp． the topological degree theory）， —the Lefschetz and the Nielsen theories both in absolute and relative cases， —periodic point theorems， —topological essentiality， —continuation—type theorems． All the above topics are related to various classes of mappings including compact absorbing contractions and condensing maps． Besides the （more powerful） homological approach， the approximation techniques are alternatively employed as well．

编辑推荐

《用于边界值问题的拓扑不动点原理》利用不动点理论求微分方程的解，独具特色。目次：理论背景；一般原理；在微分方程中的应用。

用户评论 (总计1条)

•   很好的书，有用，仔细学习